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Aug 22, 2011 at 19:46 comment added The Bridge Well even if increments exhibit high moments, you can still extend the diffusion framework to so-called stochastic volatility, which is an active area of estimation under the additional constraint of Hidden Markov process. Regards
Aug 22, 2011 at 18:42 comment added Simon Lyons My personal feeling is that financial time series aren't modelled particularly well by diffusion processes. Increments tend to exhibit high kurtosis, which means they're better described with a Levy-driven SDE rather than a process with locally Gaussian increments. The Markov property can potentially cause problems, too.
Aug 22, 2011 at 18:00 history answered ShawnD CC BY-SA 3.0